Barack Obama, the US president, has urged India to step up its dialogue with Pakistan to help to secure the region’s stability, warning that efforts to combat extremism in India’s nuclear-armed neighbour have not progressed as quickly as Washington had hoped.

Mr Obama, on a three-day visit to India, called on Sunday for New Delhi to revive a dialogue with Islamabad badly set back by the 2008 terror attacks on Mumbai by Pakistani militants.

“My hope is that over time trust develops between the two countries, that dialogue begins,” he told students at St Xavier’s College. “Ultimately India and Pakistan have to arrive at their own understandings”.

Mr Obama cautioned that the economic success that India was enjoying would be imperilled by an unstable region where militant insurgencies raged in Pakistan and Afghanistan, where US troops are fighting the Taliban.

“The country that has the biggest stake in Pakistan’s success is India. I think that if Pakistan is unstable that is bad for India. If Pakistan is stable and prosperous that’s good,” he said.

Mr Obama recommended the two rivals start talking about the “less controversial issues” and then build up to tougher issues, such as the disputed territory of Kashmir, over which the two have fought three wars over the past 63 years.

Manmohan Singh, India’s prime minister, believes the two countries have shared destinies, and has stressed that India poses no threat to Pakistan in an effort to scale down military forces on the border.

Yet Mr Obama’s emphasis of linkages between Pakistan and India, which were separated at the end of British rule in 1947, is highly sensitive. Many Indian leaders gauge the growing maturity of New Delhi’s relationship with Washington by what they call the “de-hyphenation” of India and Pakistan in recognition of India as a global power and vibrant economy.

New Delhi is suspicious of US military assistance to Pakistan and is uneasy about Washington identifying any role for Islamabad in bringing stability to Afghanistan and brokering talks with the Taliban.

Mr Obama warned that Pakistan was confronted by a “profound problem” and that its progress towards eradicating extremism was “not as quick as we would like”. He said that his administration was “engaging aggressively” with the Pakistani government to bring peace and stability.

“There’s a need to look for practical steps . . . Living in the past simply won’t work,” said Stephen Cohen, a senior fellow at the Brookings Institution, in Washington.

“I see a 100 years of conflict between India and Pakistan looking ahead.”

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